Vol. 9, No. 9, 2015

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Families of nearly ordinary Eisenstein series on unitary groups

Appendix: Kai-Wen Lan

Vol. 9 (2015), No. 9, 1955–2054
Abstract

We use the doubling method to construct $p$-adic $L$-functions and families of nearly ordinary Klingen Eisenstein series from nearly ordinary cusp forms on unitary groups of signature $\left(r,s\right)$ and Hecke characters, and prove the constant terms of these Eisenstein series are divisible by the $p$-adic $L$-function, following earlier constructions of Eischen, Harris, Li, Skinner and Urban. We also make preliminary computations for the Fourier–Jacobi coefficients of the Eisenstein series. This provides a framework to do Iwasawa theory for cusp forms on unitary groups.

Keywords
Iwasawa theory, ordinary, Klingen Eisenstein series, unitary groups, $p$-adic $L$-function
Primary: 11R23
Milestones
Received: 12 February 2014
Revised: 27 June 2015
Accepted: 18 August 2015
Published: 4 November 2015
Authors
 Xin Wan Department of Mathematics Columbia University Room 509, MC 4406 2990 Broadway New York, NY 10027 United States Kai-Wen Lan School of Mathematics University of Minnesota Minneapolis, MN 55455 USA